high performance computing on graphics processing units: hgpu.org

High-fidelity geopotential calculation using spherical harmonics (SH) is expensive and relies on recursive non-parallel relations. Here, a global point mascon (PMC) model is proposed that is memory light, extremely simple to implement (at any derivative level), and is naturally amenable to parallelism. The gravity inversion problem is posed classically as a large and dense least squares estimation problem. The well known ill-conditioned nature of the inversion is overcome in part using orthogonal solution methods, a judicious choice for the mascon distribution, and numerically preferred summation techniques. A variety of resolutions are examined including PMC models with up to 30,720 mascons. Measurements are simulated using truncated SH evaluations from the GGM02C gravity field derived from the GRACE spacecraft. Resolutions are chosen in order to target residual levels at least an order of magnitude smaller than the published expected errors of the GGM02C. A single Central Processing Unit (CPU) implementation is found to be approximately equal in speed compared to SH for all resolutions while a parallel implementation on an inexpensive Graphics Processing Unit (GPU) leads to order of magnitude (13 to 16 times) speedups in the case of a 156×156 gravity field. A single CPU Matlab implementation is competitive in speed with compiled code due to Matlab’s efficient use of large matrix operations.